Simplify the following expression: $z = \dfrac{-7a^2 + 84a - 140}{a - 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ z =\dfrac{-7(a^2 - 12a + 20)}{a - 2} $ Then we factor the remaining polynomial: $a^2 {-12}a + {20} $ ${-2} {-10} = {-12}$ ${-2} \times {-10} = {20}$ $ (a {-2}) (a {-10}) $ This gives us a factored expression: $\dfrac{-7(a {-2}) (a {-10})}{a - 2}$ We can divide the numerator and denominator by $(a + 2)$ on condition that $a \neq 2$ Therefore $z = -7(a - 10); a \neq 2$